In his Essay concerning Human Understanding, John Locke explicitly refers to Newton’s Philosophiae naturalis principia mathematica in laudatory but restrained terms: “Mr. Newton, in his never enough to be admired Book, has demonstrated several Propositions, which are so many new Truths, before unknown to the World, and are farther Advances in Mathematical Knowledge” (Essay, 4.7.3). The mathematica of the Principia are thus acknowledged. But what of philosophia naturalis? Locke maintains that natural philosophy, conceived as natural science (as opposed to natural (...) history), would give us demonstrations of the necessary connection between the (ultimately, simple) ideas constitutive of our complex ideas of various natural kinds of substances (e.g., gold). Indeed Locke goes so far as to suggest that a completely adequate natural science would also realize (perhaps, per impossibile) the goal of transforming the corpuscularian hypothesis into knowledge by demonstrating the necessary connection between the ‘microstructure’ (primary qualities of insensible corpuscles) of a particular natural kind of substance (e.g., gold) and the ideas of secondary qualities constitutive of the complex idea of that kind of substance. Locke’s conclusion concerning the possibility of the development of a natural science thus conceived is pessimistic: In vain therefore shall we endeavor to discover by our Ideas, (the only true way of certain and universal knowledge,) what other Ideas are to be found constantly joined with that of our complex Idea of any Substance: since we neither know the real Constitution of the minute Parts, on which their Qualities do depend; not, did we know them could we discover any necessary connexion between them, and any of their Secondary Qualities: which is necessary to be done, before we can certainly know their necessary co-existence (Essay, 4.3.14). It is understandable that, with such a conception of the science of nature, Locke found little of it in Newton’s Principia. In this paper, I further explore what might, perhaps with some hyperbole, be termed Locke’s ‘disappointment’ with the Prinicipia as a contribution to natural science. In particular, I argue that Locke’s adherence to the idealist epistemology of the Way of Ideas entails that mathematics cannot lend its certainty as a scientia to natural philosophy. Consequently, he finds more mathematics than natural philosophy in the Principia. (shrink)

The “Aristotelian” conception of human agency and responsibility locates agency and responsibility in the exercise of practical reason in deliberation. A characteristic of such deliberation is that it must pertain to matters that can be decided either one way or the other. Some of Aristotle’s texts suggest an interpretation of deliberation that appears to yield the paradoxical result that agents are most responsible for (or act most freely with respect to) choices that are least determined, to the exclusion of other (...) possible choices, by the practical reasoning issuing in those choices. This essay explores this strand of thought in Aristotle. It then proceeds to examine the response to the “paradox” in a middle-Platonist work, the De fato of Pseudo-Plutarch, and in the thought of the eminenttwentieth-century neo-Thomist, Reginald Garrigou-Lagrange. (shrink)

A Master-like argument, in the usage of the present paper, is an argument that employs a reductio ad impossibile principle to transmit the necessity of what are or become past truths to the remainder of time by means of necessary conditionals of some sort. The conclusion of such an argument is some no-unactualized-possibilities principle. This paper argues that the formulation of a Master-like argument by A. N. Prior in a mixed modal temporal propositional logic introduces certain artifacts into the logical (...) analysis of the argument. One of these, a principle of temporal discreteness, is not essential to a Master-like argument. Another, a principle of forwards temporal linearity, is technically essential; but it is usually tacitly presupposed by the necessary temporal conditionals employed to 'tie together' past and future time in less formal accounts of Master-like arguments. (shrink)

This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The Aristotelian model is presented as an application of the ancient, geometrically orthodox conception of extension to the physical world. The other two models, which represent departures from mathematical orthodoxy, are a "quantum" model of spatial magnitude, and a Stoic model, according to which limit entities such as points, edges, and surfaces do not exist in (physical) reality. The book is unique in its (...) discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments. (shrink)

This paper begins by pointing out that the Aristotelian conception of continuity (synecheia) and the contemporary topological account share the same intuitive, proto-topological basis: the conception of a ?natural whole? or unity without joints or seams. An argument of Aristotle to the effect that what is continuous cannot be constituted of ?indivisibles? (e.g., points) is examined from a topological perspective. From that perspective, the argument fails because Aristotle does not recognize a collective as well as a distributive concept of a (...) multiplicity of points. It is the former concept that allows contemporary topology to identify some point sets with spatial regions (in the proto-topological sense of this term). This identification, in turn, allows contemporary topology to do what Aristotle was unwilling to do: to conceive the property of continuity, as well as the properties of having measure greater than zero and having n- dimension, as emergent properties. Thus, a point set can be continuous (connected) although none of its subsets of sufficiently smaller cardinality can be. Finally, the paper discusses the manner in which a topological principle, viz., the principle that none of the singletons of points of a continuum can be open sets of that continuum, captures certain aspects of the Aristotelian proto-topological conception of the relation between points and continua. E.g., for both Aristotle and contemporary topology, points in a continuum exist simple as limits of the remainder of the continuum: their singletons have empty ?interiors? and, hence, they are not ?chunks? (topologically, regular closed set) of the continuum. (shrink)

This note fleshes in and generalizes an argument suggested by W. Salmon to the effect that the addition of a requirement of mathematical randomness to his requirement of physical homogeneity is unimportant for his ontic account of objective homogeneity. I consider an argument from measure theory as a plausible justification of Salmon''s skepticism concerning the possibility that a physically homogeneous sequence might nonetheless be recursive and show that this argument does not succeed. However, I state a principle (the Generalized Salmon (...) Thesis) that is intuitively plausible and reflects this skepticism. The principle entails that one should be just as certain that the limit of such an infinite sequence is irrational as one is certain that the sequence is not computable. But I claim that this consequence is acceptable. (shrink)

This paper develops an interpretation of the fourth account of conditionals in Sextus Empiricus's Outlines of Pyrrhonism that conceptually links it with contemporary ?relevance? interpretations of entailment. It is argued that the third account of conditionals, which analyzes the truth of a conditional in terms of the joint impossibility of antecedent and denial of consequent, should not be interpreted in terms of a relative incompatibility of antecedent and denial of consequent because of Stoic acceptance of the truth of some conditionals (...) of the form p ? ?p and its converse. Rather, it is suggested, ancient attempts to avoid the so-called paradoxes of implication involve the fourth account of conditionals. I hypothesize that this account is related to Stoic attempts to define truth conditions for conditionals in terms of a theory of the concludency (validity) of arguments in opposition to the more common procedure (represented by the first three accounts of conditionals) of specifying truth conditions for conditionals ?semantically? and using those truth conditions in the development of a theory of argument validity. (shrink)

A well-known epigram by Callimachus on the philosopher Diodorus Cronus reads as follows:The question of the third line, while perhaps recondite from a contemporary perspective, was clear in antiquity. The crows are asking ‘What follows ?’, in allusion to the Hellenistic disputes concerning the truth conditions of conditional propositions , disputes in which the views of Diodorus figured prominently.I agree with Sedley that the question of the last line is ‘much more problematic’. The common interpretation has been to read the (...) αθι as a form of αθις and to interpret it temporally. The result, in Pfeiffer's estimation, is ‘quomodo posthac erimus?’.This interpretation derives from Sextus Empiricus' discussion at M. 1.309–12 of the last two lines of the epigram. After crediting the grammarian with the ability to understand the allusion in the crows' first question , he proceeds to argue that the philosopher has a better chance than the grammarian of understanding the second question. But, to quote Sedley, Sextus ‘makes a ghastly mess of it’ when he attempts his own elucidation. According to an argument of Diodorus, a living thing does not die in the time in which it lives nor in a time in which it does not live. Hence, Sextus concludes, it must be the case that it never dies and, ‘if this is the case, we are always living and, according to him, we shall come to be hereafter ’. (shrink)

This paper specifies classes of framesmaximally omnitemporally characteristic for Thomas' normal modal logicT 2 + and for each logic in the ascending chain of Segerberg logics investigated by Segerberg and Hughes and Cresswell. It is shown that distinct a,scending chains of generalized Segerberg logics can be constructed from eachT n + logic (n 2). The set containing allT n + and Segerberg logics can be totally- (linearly-) ordered but not well-ordered by the inclusion relation. The order type of this ordered (...) set is *( + 1). Throughout the paper my approach is fundamentally semantical. (shrink)

This paper discusses the 'master argument' of diodorus cronos from a semantic perspective. An argument is developed which suggests that proposition (1), 'every proposition true about the past is necessary', May have provided the principal motivation for diodorus denial of proposition (3), I.E., His equation of possibility with present-Or-Future truth. It is noted that (1) and (3) are jointly inconsistent only given the assumption of a linear ordering of time. It is further noted that diodorus' fatalism "could" be employed to (...) justify this additional assumption. However, To then use the conclusion of the 'master' to argue for fatalism would obviously be circular. I suspect, Rather, That diodorus' assumption of temporal linearity was implicit and uncritical. (shrink)

THIS PAPER PRESENTS THE SEMANTIC THEORY FOR A TEMPORAL-MODAL LOGIC WITH RIGIDLY REFERENTIAL TEMPORAL OPERATORS ('dtomorrow' AND 'dnow') IN WHICH THE 'TRADITIONAL' INDETERMINIST INTERPRETATION OF ARISTOTLE'S _DE INTERPRETATIONE 9 CAN BE MODELED. THIS LOGIC HAS, I BELIEVE, SOME INTRINSIC PHILOSOPHICAL INTEREST AND PLAUSIBILITY. HOWEVER, THE PRESENT PAPER IS PRINCIPALLY DEVOTED TO AN INITIAL EXAMINATION OF THE RELATION BETWEEN THE LOGIC AND SUCH TOPICS IN THE ANCIENT PHILOSOPHY OF THE TIME AND OF THE MODALITIES AS THE NECESSITY OF THE PAST, ABSOLUTE (...) VERSUS TEMPORALLY RELATIVE ALETHIC MODALITIES, THE 'PLENITUDE' PRINCIPLE AND UNACTUALIZED POSSIBILITIES, AND THE CYCLICAL NATURE OF TIME. (shrink)